If the Imam made a wrong intention and then repeated it, must the congregants repeat theirs?

The intention (niyyah) is a pillar of prayer (salat); prayer is not valid without it. The intention for prayer must be specified (e.g., intending to pray Dhuhr), its place is the heart, and its time is at the beginning of the prayer or slightly before it. If the imam enters the prayer with an incorrect intention, his prayer is invalid, and he must repeat it. As for the congregants (ma'mumoon), their prayer is valid if the imam did not exit his prayer but merely corrected his intention, because the reason for invalidity on the imam is something hidden from the congregants. However, if the imam made a mistake in the intention and corrected the mistake before entering the prayer, then the prayer of everyone is valid.